After one minute there is

y gallons in the tank 2, so the capacity of the tank 2 is

2(x-y) gallons.

Obviously, each minute the tank 1 is filled with

x-y gallons of water, and tank 2 is filled with

y gallons.

Let A is the number of minutes after which the 1 tank is full, and B is the number of minutes after which 2 the 2 tank is full.

Then:

A(x-y)=zBy=2(x-y) A=\frac{z}{x-y} B=\frac{2(x-y)}{y}We need to compare A and B, so we are comparing

\frac{z}{x-y} and

\frac{2(x-y)}{y} \frac{z}{x-y} ...

\frac{2(x-y)}{y} yz ...

2(x-y)(x-y)yz ...

2x^2-4xy+2y^2If (1) is true, then

yz< 2x^2-4xy-y^2Since

2x^2-4xy+2y^2> 2x^2-4xy-y^2, then

yz <2x^2-4xy+2y^2 and we are able to compare two time periods. The statement (1) alone is susfficient.

If (2) is true, then

2(x-y)<0.5z\frac{z}{x-y}>4This means that

A>4However,

B=\frac{2(x-y)}{y}, so there is no z and we only know that

x>y, but nothing could be said to compare

x-y and

y. For example, if

x=2y, then

B=2 and

A>B. However, if

x=5y, then

B=8 and we could not compare A and B.

So, the answer is (A)

NOTE: You should post DS problems in the other forum.

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